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Settino J, Lo Gullo N, Plastina F, Minguzzi A. Exact Spectral Function of a Tonks-Girardeau Gas in a Lattice. PHYSICAL REVIEW LETTERS 2021; 126:065301. [PMID: 33635692 DOI: 10.1103/physrevlett.126.065301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Accepted: 01/08/2021] [Indexed: 06/12/2023]
Abstract
The single-particle spectral function of a strongly correlated system is an essential ingredient to describe its dynamics and transport properties. We develop a method to evaluate exactly the spectral function for a gas of one-dimensional bosons with infinitely strong repulsions valid for any type of external confinement. Focusing on the case of a lattice confinement, we find that the spectral function displays three main singularity lines. One of them is due uniquely to lattice effects, while the two others correspond to the Lieb-I and Lieb-II modes occurring in a uniform fluid. Differently from the dynamical structure factor, in the spectral function the Lieb-II mode shows a divergence, thus providing a route to probe such mode in experiments with ultracold atoms.
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Affiliation(s)
- J Settino
- Dipartimento di Fisica, Università della Calabria, I-87036 Arcavacata di Rende (CS), Italy
- CNR-SPIN, I-84084 Fisciano (Salerno), Italy
| | - N Lo Gullo
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland
| | - F Plastina
- Dipartimento di Fisica, Università della Calabria, I-87036 Arcavacata di Rende (CS), Italy
- INFN, gruppo collegato di Cosenza, I-87100 Cosenza, Italy
| | - A Minguzzi
- Univ. Grenoble-Alpes, CNRS, LPMMC, 38000 Grenoble, France
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Compact chip-scale guided cold atom gyrometers for inertial navigation: Enabling technologies and design study. ACTA ACUST UNITED AC 2019. [DOI: 10.1116/1.5120348] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Polo J, Dubessy R, Pedri P, Perrin H, Minguzzi A. Oscillations and Decay of Superfluid Currents in a One-Dimensional Bose Gas on a Ring. PHYSICAL REVIEW LETTERS 2019; 123:195301. [PMID: 31765184 DOI: 10.1103/physrevlett.123.195301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Revised: 07/22/2019] [Indexed: 06/10/2023]
Abstract
We study the time evolution of a supercurrent imprinted on a one-dimensional ring of interacting bosons in the presence of a defect created by a localized barrier. Depending on interaction strength and temperature, we identify various dynamical regimes where the current oscillates, is self-trapped, or decays with time. We show that the dynamics is captured by a dual Josephson model and involve phase slips of thermal or quantum nature.
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Affiliation(s)
- Juan Polo
- University Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Romain Dubessy
- Laboratoire de Physique des Lasers, CNRS, Université Paris 13, Sorbonne Paris Cité, 99 Avenue J.-B. Clément, F-93430 Villetaneuse, France
| | - Paolo Pedri
- Laboratoire de Physique des Lasers, CNRS, Université Paris 13, Sorbonne Paris Cité, 99 Avenue J.-B. Clément, F-93430 Villetaneuse, France
| | - Hélène Perrin
- Laboratoire de Physique des Lasers, CNRS, Université Paris 13, Sorbonne Paris Cité, 99 Avenue J.-B. Clément, F-93430 Villetaneuse, France
| | - Anna Minguzzi
- University Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
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Polo J, Ahufinger V, Hekking FWJ, Minguzzi A. Damping of Josephson Oscillations in Strongly Correlated One-Dimensional Atomic Gases. PHYSICAL REVIEW LETTERS 2018; 121:090404. [PMID: 30230871 DOI: 10.1103/physrevlett.121.090404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Indexed: 06/08/2023]
Abstract
We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle-number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength, and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Because of the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states.
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Affiliation(s)
- J Polo
- Univ. Grenoble Alpes, CNRS, LPMMC, F-38000 Grenoble, France
| | - V Ahufinger
- Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
| | - F W J Hekking
- Univ. Grenoble Alpes, CNRS, LPMMC, F-38000 Grenoble, France
| | - A Minguzzi
- Univ. Grenoble Alpes, CNRS, LPMMC, F-38000 Grenoble, France
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Cominotti M, Rossini D, Rizzi M, Hekking F, Minguzzi A. Optimal persistent currents for interacting bosons on a ring with a gauge field. PHYSICAL REVIEW LETTERS 2014; 113:025301. [PMID: 25062201 DOI: 10.1103/physrevlett.113.025301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2013] [Indexed: 06/03/2023]
Abstract
We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U(1) gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction, and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.
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Affiliation(s)
- Marco Cominotti
- Université Grenoble Alpes, LPMMC, F-38000 Grenoble, France and CNRS, LPMMC, F-38000 Grenoble, France
| | - Davide Rossini
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Matteo Rizzi
- Institut für Physik, Johannes-Gutenberg-Universität Mainz, Staudingerweg 7, D-55099 Mainz, Germany
| | - Frank Hekking
- Université Grenoble Alpes, LPMMC, F-38000 Grenoble, France and CNRS, LPMMC, F-38000 Grenoble, France
| | - Anna Minguzzi
- Université Grenoble Alpes, LPMMC, F-38000 Grenoble, France and CNRS, LPMMC, F-38000 Grenoble, France
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Vignolo P, Minguzzi A. Universal contact for a Tonks-Girardeau gas at finite temperature. PHYSICAL REVIEW LETTERS 2013; 110:020403. [PMID: 23383878 DOI: 10.1103/physrevlett.110.020403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2012] [Indexed: 06/01/2023]
Abstract
We determine the finite-temperature momentum distribution of a strongly interacting 1D Bose gas in the Tonks-Girardeau (impenetrable-boson) limit under harmonic confinement and explore its universal properties associated to the scale invariance of the model. We show that, at difference from the unitary Fermi gas in three dimensions, the weight of its large-momentum tails--given by Tan's contact--increases with temperature and calculate the high-temperature universal second contact coefficient using a virial expansion.
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Affiliation(s)
- Patrizia Vignolo
- Université de Nice-Sophia Antipolis, Institut Non Linéaire de Nice, CNRS, 1361 route des Lucioles, 06560 Valbonne, France
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Zöllner S, Meyer HD, Schmelcher P. Few-boson dynamics in double wells: from single-atom to correlated pair tunneling. PHYSICAL REVIEW LETTERS 2008; 100:040401. [PMID: 18352242 DOI: 10.1103/physrevlett.100.040401] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2007] [Indexed: 05/26/2023]
Abstract
We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.
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Affiliation(s)
- Sascha Zöllner
- Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany.
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Pezer R, Buljan H. Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wave packet. PHYSICAL REVIEW LETTERS 2007; 98:240403. [PMID: 17677946 DOI: 10.1103/physrevlett.98.240403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2006] [Indexed: 05/16/2023]
Abstract
The momentum distribution (MD) dynamics of a Tonks-Girardeau (TG) gas is studied in the context of Bragg reflections of a many-body wave packet. We find strong suppression of a Bragg reflection peak for a large and dense TG wave packet; our observation illustrates the dependence of the MD on the interactions and wave function symmetry. The MD is calculated from the reduced single-particle density matrix (RSPDM). We develop a method for calculating the RSPDM of a TG gas, which is operative for a large number of particles, and does not depend on the external potential and the state of the system. The method is based on a formula expressing the RSPDM via a dynamically evolving single-particle basis.
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Affiliation(s)
- R Pezer
- Faculty of Metallurgy, University of Zagreb, Aleja narodnih heroja 3, 44000 Sisak, Croatia
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Rigol M, Muramatsu A. Emergence of quasicondensates of hard-core bosons at finite momentum. PHYSICAL REVIEW LETTERS 2004; 93:230404. [PMID: 15601131 DOI: 10.1103/physrevlett.93.230404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2004] [Indexed: 05/24/2023]
Abstract
An exact treatment of the nonequilibrium dynamics of hard-core bosons on one-dimensional lattices shows that, starting from a pure Fock-state, quasi-long-range correlations develop dynamically, and lead to the formation of quasicondensates at finite momenta. Scaling relations characterizing the quasicondensate and the dynamics of its formation are obtained. The relevance of our findings for atom lasers with full control of the wavelength by means of a lattice is discussed.
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Affiliation(s)
- Marcos Rigol
- Institut für Theoretische Physik III, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
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Berman GP, Borgonovi F, Izrailev FM, Smerzi A. Irregular dynamics in a one-dimensional Bose system. PHYSICAL REVIEW LETTERS 2004; 92:030404. [PMID: 14753854 DOI: 10.1103/physrevlett.92.030404] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2003] [Indexed: 05/24/2023]
Abstract
We study many-body quantum dynamics of delta-interacting bosons confined in a one-dimensional ring. Main attention is paid to the transition from the mean-field to the Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wave function and the momentum distribution depend on time for weak and strong interactions. We show that the transition from regular (quasiperiodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime, the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.
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Affiliation(s)
- G P Berman
- Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Girardeau MD. Dynamics of Lieb-Liniger gases. PHYSICAL REVIEW LETTERS 2003; 91:040401. [PMID: 12906646 DOI: 10.1103/physrevlett.91.040401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2003] [Indexed: 05/24/2023]
Abstract
It is proved that the Lieb-Liniger cusp condition implementing the delta function interaction in one-dimensional Bose gases is dynamically conserved under phase imprinting by pulses of arbitrary spatial form, and the subsequent many-body dynamics in the thermodynamic limit is expressed approximately in terms of solutions of the time-dependent single-particle Schrödinger equation for a set of time-dependent orbitals evolving from an initial Lieb-Liniger-Fermi sea. As an illustrative application, a generation of gray solitons in a Lieb-Liniger gas on a ring by a phase-imprinting pulse is studied.
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Affiliation(s)
- M D Girardeau
- Optical Sciences Center, University of Arizona, Tucson, Arizona 85721, USA.
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